Cooperation of N- and C-terminal substrate transmembrane domain segments in intramembrane proteolysis by γ-secretase

Intramembrane proteases play a pivotal role in biology and medicine, but how these proteases decode cleavability of a substrate transmembrane (TM) domain remains unclear. Here, we study the role of conformational flexibility of a TM domain, as determined by deuterium/hydrogen exchange, on substrate cleavability by γ-secretase in vitro and in cellulo. By comparing hybrid TMDs based on the natural amyloid precursor protein TM domain and an artificial poly-Leu non-substrate, we find that substrate cleavage requires conformational flexibility within the N-terminal half of the TMD helix (TM-N). Robust cleavability also requires the C-terminal TM sequence (TM-C) containing substrate cleavage sites. Since flexibility of TM-C does not correlate with cleavage efficiency, the role of the TM-C may be defined mainly by its ability to form a cleavage-competent state near the active site, together with parts of presenilin, the enzymatic component of γ-secretase. In sum, cleavability of a γ-secretase substrate appears to depend on cooperating TM domain segments, which deepens our mechanistic understanding of intramembrane proteolysis.


Supplementary Note 1
The origin of biphasic DHX. To explain the origin of biexponential, or biphasic, DHX, we reiterate that exchange at a given amide within a population of TMDs is dominated by the EX2 regime where the local folding rate vastly exceeds the chemical rate constant, resulting in non-correlated exchange events 1 as previously shown by demonstrating a gradual mass shift of the isotopic envelope of the C99 TMD peptide 2 . In addition to those non-correlated exchange events, we propose that very unstable regions of our TMD helices, such as a glycine-rich hinge or frayed helix termini, may undergo rare correlated exchange of two (or even more) neighboring deuterons, i.e. limited EX1 exchange 3 in addition to the prevalent EX2 regime. Mixed EX1/EX2 modes of amide exchange have been demonstrated previously to describe local protein fluctuations 4,5 . The abundance our peptides having undergone correlated DHX is apparently too low for visibly affecting the isotope pattern produced by the prevalent non-correlated DHX. Nonetheless, the superposition of isotope patterns resulting from EX1 and EX2 exchange occuring in parallel is predicted to mimic slightly reduced average masses at two neighboring positions when applying the fitting procedure (assuming the most likely case of two neighboring correlated exchange events) . This is expected to translate into artificially accelerated DHX kinetics over time. However, accelerated exchange is expected only within the initial periods of the exchange reaction where neighboring amide deuterons are abundant enough for correlated DHX to give rise to correlated exchange of deuterons. At later time points, where ongoing DHX has reduced the numbers of neighboring deuterons, correlated DHX/HDX is expected to replace correlated DHX, thus producing less artificial acceleration of the kinetics. As a result, at later time points of the reaction, we expect kinetics that cannot be distinguished from EX2, allowing us to calculate G values from the data. We note that these slow parts of the biphasic kinetics cover the major fraction in most cases where amide deuterons exhibit biphasic exchange, as reflected by the respective population sizes A (fast part) and B (slow part) (Table S2; see Methods). To illustrate the point, Fig. S2 shows mixed EX1 and EX2 kinetics and its consequences using an idealized model peptide.
In sum, this model is well suited to explain fast initial exchange kinetics followed by slower kinetics at highly flexible regions of a helix. We infer that the slow parts of the kinetics allow us to calculate accurate thermodynamic stabilities at unstable sites. Moreover, we propose that the apparent existence of correlated exchange events may indicate slow backfolding events after local helix unfolding.

Potential impact of experimental conditions on calculated H-bond strength.
Exchange rate constants k exp are transformed into G values by relating them to the rates k ch of chemical exchange of unfolded peptides. In general, amides where k ch values from the literature exceed the k exp 6 are protected from exchange depending on their H-bond strength. We note that k ch may be lower under our conditions than the standard values for several potential reasons: (i) The molarity of water in 80% (v/v) TFE solvent is only 20% of the bulk molarity used for the determination of the reference chemical exchange rates k ch ; (ii) the hydration of residues in the hydrophobic core of a TMD dissolved in 80% TFE may be reduced relative to bulk water; (iii) k ch values determined for model tripeptides in the unfolded state may not correctly represent sterical hindrance of exchange in the helical state; and (iv) TFE might have an impact on the autoionization constant of water and k ch 7 . As a result, our calculated G values might be underestimating the true values to some extent.

Supplementary Note 2: Statistics in the Analysis of Amide Exchange Kinetics.
It is assumed that exchange data are available for N exchange periods t n (n=1, 2, …, N). To analyze the exchange kinetics of the amide hydrogen of amino acid m, the first step consists in the determination of the mean numbers D mean (m,n) of the D numbers D m obtained for all the fragment types analyzed for time point n.
The main model employed for the analysis of the kinetics predicts a first order reaction that leads from the starting value D start of the D number to the asymptotic D number D asymptotic . The experimental rate constant k exp,m for the exchange of amide hydrogen m is determined by a nonlinear least squares fitting routine that minimizes the quantity  2 of equation (1a): m,n m,n mean fit n1 fit asymptotic start asymptotic exp,m n (15a) with : D (m, n) D (m, n) and For amide hydrogens exhibiting a biphasic exchange dynamics, the quantity  2 of equation (1b) is minimized to determine the rate constants k 1 exp,m , k 2 exp,m and the ratio A of the conformation exhibiting the rate constant k 1 exp,m : For H/D and D/H exchange, the number D start amounts to 0 and 1, respectively. In case some of the numbers D mean (m,n) are not available due to missing fragments for certain time points, the fitting procedure is restricted to the time points with available D numbers. For the fitting to be performed, the number of time points with D numbers must not be smaller than three and six for monophasic and biphasic behavior, respectively.
To estimate the standard errors of the fitted quantities (monophasic behavior: k exp,m , biphasic behavior: k 1 exp,m , k 2 exp,m and A), the standard deviation  m is calculated for the residuals  m,n obtained for the best fit. The standard deviation  m is then used to perform the fitting defined in (1a) or (1b) for additional 2N sets of D numbers: The uncertainty  m,n of the decimal logarithm of the rate constant k exp,m that is caused by the uncertainty  m of the numbers D mean (m,n) is estimated as the mean of the two numbers |log[k exp,m ]log[k(Set n-1)]| and |log[k exp,m ]-log[k(Set n-2)]|. The quantities k(Set n-1) and k(Set n-2) stand for the best fit rate constants obtained with the sets of D-numbers Set n-1 and Set n-2, respectively. By error propagation, the standard error log(k exp,m ) of the decimal logarithm of the experimental rate constant k exp,m is calculated in the following way: In case of a biexponential fit, the uncertainties  1 m,n and  2 m,n of the decimal logarithms of the rate constants k 1 exp,m and k 2 exp,m , respectively, are estimated in full analogy to the estimation of  m,n . The standard errors log(k 1 exp,m ) and log(k 2 exp,m ) are calculated in the following way: 1 exp,m 1 m,n 2 exp,m 2 m,n n 1 n 1 (16b) log k , log k .
To estimate the uncertainty of the relative abundance of the conformation with the rate constant k 1 exp,m , the means A m,n of the two numbers |A ,m -A(Set n-1)| and |A ,m -A(Set n-2)| are calculated with A(Set n-1) and A(Set n-2) standing for the ratios obtained with the sets of D-numbers Set n-1 and Set n-2, respectively. By error propagation, the standard error A ,m of the experimental ratio A ,m is calculated as follows: In cases where k ch,m is available, the experimental rate constant k exp,m can be used to calculate the difference G m of the Gibbs Free Energy associated with the equilibrium between the effectively folded and the effectively unfolded situation for amide hydrogen m. If the rate constant of the unfolding reaction of the peptide, which leads to an exchange competent state of amide hydrogen m, is denoted by k m,+ , and if the rate constant of the reverse reaction that makes the amide hydrogen m not exchange competent is denoted by k m,-, G m is given by equation (4): According to equation (5), the fraction k m,+ /( k m,+ + k m,-) can be determined from the experimental rate constant k exp,m and the chemical rate constant k ch,m : The limits of the standard confidence interval of G m are calculated by means of the standard error log(k exp,m ) of the decimal logarithm of k exp,m using equations (7): In case of a biexponential fit, instead of being performed with k exp,m , the calculation of G m , G m,min and G m,max is based on the smaller of the two rate constants k 1 exp,m and k 2 exp,m .
The plausibility of the biexponential fit is tested by means of the hypotheses H0 and H1: H0 means that the exchange behavior is monoexponential, whereas H1 means that it is biexponential. For both the hypotheses H0 and H1, the likelihood values λ0 and λ1 are calculated, respectively. The calculation is based on the assumption that the D mean(m,n) numbers follow Gaussian distributions centered around D fit(m,n) and with standard deviations amounting to σ m for all exchange periods. The standard deviation σ m is estimated by means of the residuals of the fitting procedure. As a consequence, the values λ0 and λ1 are calculated according to the equations (8a) and (8b), respectively: In order to apply Wilks' theorem, the likelihood values λ0 and λ1 are used for the calculation of the test statistic T: Since the biexponential fit implies three parameters (degrees of freedom d1=3), whereas the monoexponential fit implies only a single parameter (degrees of freedom d0=1), the non-negative likelihood ratio λ0/λ1 is smaller than 1. This means that T is always greater than or equal to zero. In order to decide whether T is not significantly greater than zero, i.e. the hypothesis H0 is to be accepted, the test statistic T is compared with its probability distribution. According to Wilks' theorem, this probability distribution is approximately a χ2 distribution with degrees of freedom equal to d3-d1=2 ( 1− 0=2 2 ). The p-value for the validity of H0 is equal to the probability to observe values of the test statistic greater than or equal to T. Since 1− 0=2 2 is an exponential distribution with the rate parameter 1/2, the p-value (p) for the validity of H0, i.e. a monoexponential behavior is calculated as follows: Ac-KKKLIAAGVIGGLFILVIVGLTFAVYVKKK-NH 2

Notch1
Ac-KKKLHFMYVAAAAFVLLFFVGCGVLLSKKK-NH 2  where each residue has a mass of 101 Da after deuteration of its amide. After a given period x of exchange we assume that residues A and D exchange 0.3 D by EX2 while residues B and C exchange a total of 0.4 D by low abundance EX1 (0.1 D) superimposed onto prevalent EX2 (0.3 D). The mass differences at the different residues are obtained by subtraction of the different c and z fragments (as obtained by ETD) from each others. Note the higher mass difference of 0.4 D at residues B and C which is expected to lead to an accelerated exchange rate constant k exp calculated for an early phase of DHX, thus generating a biphasic shape of the kinetics (exemplified by that at C99 G38 taken from Fig. S3). At later time points, DD neighbors will have been replaced by DH neighbors where EX1 DHX cannot be distinguished from EX2. Figure 4. Residue-specific amide DHX kinetics of C99 derivatives. The calculated deuterium contents D (mean values, N = 3) of the respective amides are plotted against the exchange period t. The shown kinetics were used to calculate the respective k exp values after data fitting with monoexponential or biexponential decay functions. Fitting was only performed for those kinetics that were deemed complete enough for calculating k exp . Sequence positions (Aβ numbering) are given in the insets; the amino acid type at a given position corresponds to the wt C99 sequence. C99 data are taken from Fig. S1.

Supplementary
Supplementary Figure 5. DHX rate constants of TMD peptides. Rate constants k exp of constructs whose G values are depicted in Fig. 2 (a), Fig. 3 (b), or Fig. 4 (c). Shown are k exp of individual amide deuterons (filled symbols, N = 3 independent DHX reactions, log k exp ± error of fit) and the respective amide-specific intrinsic chemical exchange rate constants k ch that describe the exchange kinetics in the unfolded state 14 (emtpy symbols). Note that diverging values of k exp and k ch indicate folded regions that are partially protected from exchange.

Supplementary Figure 6. Conformational flexibility of C99 I47G/T48G and I47L/T48L mutants. (a)
Amide H-bond stabilities ΔG. The sequences feature two additional Lys residues at the N-terminus not shown here (Table S1). Aβ numbering is used and main cleavage sites are indicated. Error bars correspond to standard confidence intervals (calculated from the errors of fit in k exp determination, in some cases smaller than the symbols, N=3 independent DHX reactions). (b) Exchange rate constants k exp (filled symbols, N = 3, log k exp ± error of fit) and chemical exchange rate constants k ch (empty symbols). (c) Heat map summarizing the color-coded G values, the occurence of biphasic exchange (diamonds) and canonical γ-secretase cleavage sites (arrows). (d) Residue-specific amide DHX kinetics where the calculated deuterium contents D of the respective amides are plotted against the exchange period t. Wt C99 data are reproduced from Fig. S1.